CA Approximation of Coupled-Map Lattices

In this section, we follow Chate and Manneville s analysis of the following onedimensional CML system  

The Chate and Mamieville approximation schemes consist of finding sets of increasingly finer piece-wise linear step-function approximations of the continuous 

CML / ([chate89a], [chate89b]. When / is replaced by another discrete function /, taking on one of a finite site of distinct values, the CML defined by / and equation 8.44 effectively becomes a fc-state CA defined on the same lattice and local neighborhood structure. Of course, we are entirely free to choose any / that we desire, provided that it preserves the critical dynamical features of the original function in particular, / must preserve the absorbing character of the laminar state. 

We can continue to construct increasingly finer approximations of the original function / by iterating the above steps. Thus, the p order approximation will use the intervals 

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